If you're 25, you are still covered by your parent's health insurance for another year as long as you are on their policy. I would ask your counselor who he would recommend you see in order to get an official diagnosis, and then I would follow up directly with that person/their office in regards to what insurance they accept, what kind of time commitment you'd be looking at in terms of number of appointments, and if they would be willing to put you on a payment plan for anything not covered by your insurance. From there, you could make appointments and arrange to get to and from them.
I would also have a conversation with your parents and make it clear to them that an official diagnosis is going to be necessary for you to survive on your own as an adult, for both getting an accommodating job and potentially government benefits. They aren't going to live forever. You will need some source of income that they won't be able to provide one day, and the first step to securing that for yourself is this diagnosis. No parent wants to think about their kid being homeless or starving, especially when they have the power to prevent it.